1354182792maju-cell-2012-fall-week-11-12-fading

7/29/2019 1354182792MAJU-Cell-2012-Fall-Week-11-12-Fading

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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan

Dr. Noor M KhanEE, MAJUMulti-Path FadingChannel 1EE6763Cellular Mobile CommunicationsWeek 11-12; Fall - 2012

Multi-Path FadingChannel

Base

Station

Mobile

Station

Lecturer: Assoc. Prof. Dr. Noor M. KhanDepartment of Electronic Engineering,

Muhammad Ali Jinnah University,

Islamabad Campus, Islamabad, PAKISTAN

Ph: +92 (51) 111-878787, Ext. 129

Fax: +92 (51) 2822743

email: [email protected], [email protected]

Acme Center for Research in Wireless Communications (ARWiC) Lab

www.arwic.com
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Mobile Channel Parameters

Time delay spread |

Coherence Bandwidth | -> ISI

Doppler Spread | Coherence Time | -> Unstable channel

Flat fading

Frequency selective fading Fast fading

Slow fading


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Multi-path Propagation

Multi-path smears or spreads out the signal

delay spread

Causes inter-symbol interferencelimits the maximum symbol rate

Transmitted

SymbolReceived

Symbol

Base

Statio

n

Mobile

Station

t


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Delay Spread

TransmittedSymbol ReceivedSymbol

BaseStation

MobileStation

tTime

Space


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Intersymbol Interference

TransmittedSymbol ofInterestReceivedSymbol ofInterest

t

ReceivedSymbolsTransmittedSymbols

t


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Average Delay Spread

Average delay spread

k

k

k

kk

k

k

k

kk

P

P

a

a

)(

)(

2

2

Multi-pathProfile(Discrete)

t

)(kP

00

1 2

k

)(1P

)(0P

)(2P

)(kP


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RMS Delay Spread

(Discrete) RMS delay spread

22

k

k

k

kk

k

k

k

kk

P

P

a

a

)(

)(

2

2

22

2


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Average Delay Spread

(Continuous Delay Profile)

Average delay spread

Representative delay functions

0

0

)(

)(

dttP

dttPt

elsewherezeroandttP

etP

d

t

202

)(uniform

1)(exp


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Measurements

Type ofEnvironment

Delay Spreadd(s)

Open area


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Coherence Bandwidth

Coherence bandwidth Bc is a range of frequencies

over which the channel can be considered flat

passes all spectral components with approximately equalgain and liner phase

Bandwidth where the correlation function RT() for

signal envelopes is high

Therefore two sinusoidal signals with frequenciesthat are farther apart than the coherence bandwidth

will fade independently.


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Coherence Bandwidth

If RT() > 0.9

If RT() > 0.5

An exact relationship between coherence

bandwidth & delay spread does not exist

50

1CB

5

1

C

B


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Doppler Shift

fcbroadening from fc to (fc + fm )

BS1v

cvff cm

v


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Relativistic Doppler Frequency

The observed frequency is

where the relative velocity v is positive if the source isapproaching and negative if receding.

fc- carrier freq., c-speed of light, fd-Doppler shift

c

v1

c

v1

ff c

c

vffff ccd


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Doppler Spread & Coherence

Time Describes the time varying nature of the channel

in a local area

Doppler Spread BD, is a measure of the spectralbroadening caused by the time rate of change

fcbroadening from (fc - fm) to (fc + fm )

If the base-band signal bandwidth is much greater

than BD, the effects of Doppler spread are

negligible at the receiver


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Coherence Time

Coherence Time is the time domain dual ofDoppler spread

Doppler spread and coherence time areinversely proportional

TC = 1/fm

Statistical measure of the time duration overwhich the channel impulse response isinvariant

M h d Ali Ji h U i it I l b d C P ki t


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Coherence Time

If the coherence time is defined as the time over

which the correlation function is above 0.5, then

Rule of thumb for modern digital communication

defines TC as the geometric mean of the above two

expressions for TC

m

Cf

T16

9

216

9

m

Cf

T



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Inter-symbol Interference

For no Inter-symbol Interference the

transmission rate R for a digital transmission is

limited by delay spread and is represented by:R < 1/2 ;

If R >1/2 Inter-symbol Interference (ISI)

occurs

Need for ISI removal measures (Equalizers)



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Types of Small-Scale Fading



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Small-Scale Fading

Delay Spread

Small-Scale Fading(Based on time delay spread)

Flat Fading1. BW of signal < Coherence BW of

channel

2. Delay Spread < Symbol period

Frequency Selective Fading1. BW of signal > Coherence BW of

channel

2. Delay Spread > Symbol period



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Small-Scale Fading

Time Variations

Small-Scale Fading(Based on Doppler spread)

Fast Fading1. High Doppler spread

2. Coherence time < Symbol

period

3. Channel variations faster then

base-band signal variations

Slow Fading1. Low Doppler spread

2. Coherence time > Symbol

period

3. Channel variations slower then

base-band signal variations


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Muhammad Ali Jinnah University Islamabad Campus Pakistan


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Flat Fading 2

BS >



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Frequency Selective Fading 1

If the mobile radio channel as a constant gain and

linear phase over a coherence bandwidth, smaller

than the bandwidth of the transmitted signal - thereceived signal will undergofrequency selective

fading

Again, the signal bandwidth is wider then the

channel coherence bandwidth, causing one ormore areas of attenuation of the signal within the

signal bandwidth



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Frequency Selective Fading 2

BS > BC & TS <



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Fast Fading

The channel impulse response changesrapidly within the symbol duration -

coherence time < symbol period TS > Tc and BS < BD Channel specifies as a fast or slow fading

channel does not specify whether thechannel is flat fading or frequency selectivefading



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Slow Fading

The channel impulse response changes at a ratemuch slower than the transmitted base-bandsignal.

Doppler spread is much less than the bandwidth ofthe base-band signal

TS > BD

Velocity of the MS and the base-band signalingdetermines whether a signal undergoes fast orslow fading



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Summary

Fast and slow fading deal with the

relationship between the time rate of change

in the channel and the transmitted signal,NOT with propagation path loss models



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Dr. Noor M KhanEE, MAJUMulti-Path FadingChannel 28

EE6763Cellular Mobile CommunicationsWeek 11-12; Fall - 2012

Typical Cellular Mobile Environment

Elevated BS

Antenna

MS

Remote DominantReflectors/Scatterers

(Influential)

Medium-Distance DominantReflectors/Scatterers (Influential)

Scatterers local to MS (Influential)Scatterers local to BS (Non-influential)



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Fading

Fading: The interference between two or

more versions of the transmitted signal

which arrive at the receiver at slightly

different times

Multipaths: Above mentioned versions of

the transmitted signal



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Fading (Continued)

Delay Spread Coherence Bandwidth

Frequency separation at which two

frequency components of Tx signal undergoindependent attenuations

Doppler SpreadCoherence Time

Time separation at which two time

components of Tx signal undergo

independent attenuations



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Fading (Continued)

Time

Bc

Tc

Bandwidth

Flat in Time and

Selective in Frequency

Flat in Time and

Frequency

Flat in Frequency and

Selective in Time

Selective in both

Time and Frequency



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EE6763Cellular Mobile Communications

Week 11-12; Fall - 2012

Fading (Continued)

Fast and Slow Fading

If the channel response changes within a symbol

interval, then the channel is regarded FAST FADING

Otherwise

the channel is regarded as SLOW FADING



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Week 11-12; Fall - 2012

Fast Fading

When?The channel impulse response changes rapidly within

the symbol period of the transmitted signal.

What?The Doppler Spread causes frequency dispersion

which leads to signal distortion.


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Week 11-12; Fall - 2012

Doppler Spread (Continued)

f: carrier frequency

c: speed of light

v: mobile speed

: Angle of motion with

incoming multipath

Scattering Point

Incoming

multipath

BS

MS

Line of

Sight

y

x

v



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Week 11-12; Fall - 2012


cosd

f vf

c

f: carrier frequency

c: speed of light

v: mobile speed

: Angle of motion with

incoming multipath



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Week 11-12; Fall - 2012


For the land mobile fading spectrum,

The Auto-Correlation Function Doppler Fading Spectrum



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y, p ,



Week 11-12; Fall - 2012

Doppler Spread (Continued)h is the channel impulse response

h has a complex normal distribution with zero mean|h| is Raleigh distributedPhase is uniformly distributed between 0 and 2

is Chi-square distributed



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y, p ,



Week 11-12; Fall - 2012

Fading in Brief

Large Doppler Spread

Time-Selective Fading

Large Delay Spread

Frequency-Selective Fading

Large Angle Spread

Space-Selective Fading



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y, p ,



Week 11-12; Fall - 2012



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y, p ,



Week 11-12; Fall - 2012

Rayleigh Fading 1

The received envelope (amplitude) of a flat

fading signal is described as a Rayleigh

distributionSquare root sum r, of two quadrature Gaussian

noise signals xI and yQ has a Rayleighdistribution (Papoulis65)

22

QI yxr )0(;

2exp)(

2

2

2

r

rrrp



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y p



Week 11-12; Fall - 2012

Rayleigh Fading 2



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Week 11-12; Fall - 2012

Rayleigh Fading PDF



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Dr. Noor M KhanEE, MAJUMulti-Path FadingChannel

44EE6763Cellular Mobile CommunicationsWeek 11-12; Fall - 2012

Rayleigh Fading 3

- rms value of the received voltage signal beforeenvelope detection

2 - time average power before envelope detection

The probability that the received signal envelope

does not exceed R is given by:

)0(2

exp)(2

2

2

r

rrrp

2

2

02

exp1)()Pr()(

RdrrpRrRP

R



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Rayleigh Fading 4

The median value ofris found by solving

Mean and median differ by only 0.55dB

77.1

)(21

0

median

r

r

drrpmedian



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Ricean Fading 1

When there is a dominant stationary signal

component

At the output of an envelope detector -adding a DC component ot the random

multi-path

)0,0(;)(20

2

)(2

22

rAforAr

Ier

rp

Ar

e



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Ricean Fading 2

A - peak amplitude of the dominant signal

I0 () - modified Bessel function of the first

kind and zero order

Described in terms of a Ricean factor, K

)(2

log10)( 2

2

dBAdBK



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Ricean PDF

Received signal envelope voltage r (V)

dBK

dBK 6

)(rp



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Clarks Model for Flat Fading 1

Statistical Characteristics of the EM fields of the

received signal at the MS are obtained from

scattering

Assumes

Fixed transmitter & vertically polarized antenna

Fields incident on the mobile antenna comprises of N

waves in azimuth plane with arbitrary carrier phasesand azimuth angels of arrival

equal average signal amplitude



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Clarks Model for Flat Fading 2

The model shows that the random received

signal envelope rhas a Rayleigh

distribution and is given by:

r

rrrp 0;

2

exp)(2

2

2



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Effect of Doppler Spread

It can be shown that if the angle of the received

signals, i is uniformly distributed that the

Doppler frequency has a random cosine

distribution.

Then the Doppler power spectral density S(f) can

be computed by equating the incident received

power in an angle dwith Doppler powerS(f)df dfis found by differentiating the Doppler termfmcos

wrt .



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Function of One Random

Variable

dxxfdyyf )()( XY

x - random

variable b

a

dxxf 1)(X

y - randomvariable

)(

)(

1)(

bg

ag

dyyfY

y =g(x); function of x

)(

)(

1)(

bg

ag

dyyfY

y

x

a b

)(ag

)(bg

)(xgy

)(xfX

)(yfY

x

)(xg



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Variable

dxxfdyyf )()( XY

x - random variable b

a

dxxf 1)(X

y - random variable

y =g(x); function of x y

x

a b

)(ag

)(bg

)(xgy

)(xfX

)(yfY

x

)(xg



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Variabley - random

variable )(

)(

1)(

bg

ag

dyyfY

y =g(x); function of x

y =g(x); substitution

in )(

)(

1)(

bg

ag

dyyfY

;))(()( xgfyf YY ;)(' dxxgdy

1)()('))(( b

a

b

a

dxxfdxxgxgf XY

x

a

xg

a

dxxfdxxgxgf )()('))((

)(

XY

b

a

bg

agxy

)(

)(

)(

)(

bg

agy



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Variable x

a

xg

a

dxxfdxxgxgf )()('))((

)(

XY

)()('))(( xfxgxgf XY

)()(')( xfxgyf XY

)('

)(

)( xg

xf

yfX

Y



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Doppler Shift

fc broadening from fc to (fc + fm )

v

c

vff

cm

cosmD ff



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Effect of Doppler Spread

cosmff - uniformly distributed (0,2)

'

cos

)()(

mf

SfS f

sin2

1)(

mffS f

2

cos1sin

mf

fcos

2

2

12

1)(

m

mf

ff

fS

f



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58EE6763Cellular Mobile Communications

Week 11-12; Fall - 2012

Doppler Spectrum

the incident received power at the MS depends on the

power gain of the antenna and the polarization used

2)/(1)(

mff

AfS



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Week 11-12; Fall - 2012

Two-ray Rayleigh Fading

Model Clarkes model for flat fading

It is necessary to model multi-path delay

spread as well

Commonly used model is the two-ray

model



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Week 11-12; Fall - 2012


Model



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Week 11-12; Fall - 2012


Model The impulse response of the model

.1

and .2

are independent and Rayleigh distributed

1 and 1 are independent and uniformly distributed

over [0,2]

- time delay between the two rays

By varying it is possible to create a wide range offrequency selective fading effects

)()exp()()exp( 2111 tjtjhb



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Week 11-12; Fall - 2012

Beyond Current Engineering

Practice



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Week 11-12; Fall - 2012

Antenna Arrays are

Electromagnetic Eyes



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Week 11-12; Fall - 2012

Smart Antenna System with

Multi-path

BS

nSxy



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Week 11-12; Fall - 2012

Multi-user System Model

nSxy

y - received signal (N X 1) dimensional vector

S - signature matrix (N X K) dimensional matrix

x - transmitted symbols (K X 1) dimensional vector

n - Gaussian noise (N X 1) dimensional vector

N - Number of antenna elementsK - Number ofUsers

Inn2H}{E



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Week 11-12; Fall - 2012

Multi-user System Information

Capacity

2

n

H

x2

VIlogC

SS

powersymbolSignal IxxVx PE H

power(variance)Noise2

nn

nSxy

2

n

2

1logCP



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Week 11-12; Fall - 2012

Multiuser Spatial Filter

nSxy

nxnSSSSxSSS

ySSSx

~0)()(

)(

11

1

MAI

HHHH

HH

HHSSS 1)(

Moore-Penrose

Pseudo Inverse

Optimum

Spatial

Filter



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Week 11-12; Fall - 2012

+

Array of N Elements

array axis

z

P1

1= | 1 | e j 10

1

N-1

2

12

N-1

Pk0

P1

+Pk k



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Capacity of 2G/3G vs

Achievable CapacitysHzbits //3.0

0.1

11log0.1C 2

300 / 0.3 = 1000Capacity improvement factor

sHzbits //3000.001

11log30C 2

2G/3G

3G+

1354182792maju-cell-2012-fall-week-11-12-fading

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